In a survey of 3022 adults, a poll asked people whether they smoked cigarettes a

Question

In a survey of 3022 adults, a poll asked people whether they smoked cigarettes and whether they always wear a seat belt in a car. The table shows the results of the survey. For each activity, define a success as finding an individual that participates in the hazardous activity. Complete parts (a) and (b) A. More than 5% of the population was surveyed B. The same person answered both questions C. Two questions where asked (b) Is there a significant difference in the proportion of individuals who smoke and the proportion of individuals that do not wear a seat belt? In other words, is there a significant difference between the proportion of individuals who engage in hazardous activities? Use the alpha = 0.10 level of significance. Let p_1 represent the proportion of individuals who smoke and p_2 represent the proportion of individuals that do not wear a seat belt. What are the hypotheses for this test? A. H_0: p_1 = p_2 H_1: p_1

Explanation / Answer

Given that,
sample one, x1 =499, n1 =3022, p1= x1/n1=0.165
sample two, x2 =395, n2 =3022, p2= x2/n2=0.131
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
since our test is two-tailed
reject Ho, if zo < -1.645 OR if zo > 1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.165-0.131)/sqrt((0.148*0.852(1/3022+1/3022))
zo =3.768
| zo | =3.768
critical value
the value of |z | at los 0.1% is 1.645
we got |zo| =3.768 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 3.7681 ) = 0.0002
hence value of p0.1 > 0.0002,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: 3.77
critical value: -1.645 , 1.645
decision: reject Ho
p-value: 0.0002

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